Question

FIND THE SUM OF ALL MULTIPLES OF 9 LYING BETWEEN 300-700

Answer 1

A.P. formed is 306, 315, 324, .......... , 693
Here first term = a = 306, common difference = d = 9 and last term = l = 693
693 = 306 + (n - 1)9
77 = 34 + n - 1
n = 44
Sum = n/2(a + l)
= 22(306 + 693)
= 21978

Answer 2

The multiples of 9 betwwen 300 and 700 :-

306 , 315 , 324 ,….., 693

First term = 306

Common difference = 9

nth term = 693

$\bf\huge a_{n} = a + (n - 1)d$

693 = 306 + (n - 1)9

$\bf\huge\frac{693 - 306}{9} = (n - 1)$

$\bf\huge (n - 1) = \frac{387}{9}$

(n - 1) = 43

n = 43 + 1

n = 44

Using formula :-

$\bf\huge S_{n} = \frac{n}{2}(a + l)$

$\bf\huge S_{44} = \frac{44}{2}(306 + 693)$

= 22 × 999

= 21978